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We shall present examples of Schauder bases in the preduals to thehyperfinite factors of types $\hbox{II}_1$, $\hbox{II}_\infty$,$\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively,purely infinite) setting, these systems form Schauder bases in any associatedseparable symmetric space of measurable operators (respectively, in anynon-commutative $L^p$-space).

The Haar system in the preduals of hyperfinite factors